(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Analytical Mechanics"

(54                        ANALYTICAL MECHANICS
In order to express equation (4) in terms of rectangular coordinates we replace tan 0 by (f[ and oh turn
But ds2=dx2+dy2, therefore eliminating dx between this equation and equation (5) and separating the variables
and then integrating
where a =  and c is the constant of integration.
Let the o>axis be so chosen that when .s -. o, //    , then c = 0.   Therefore
j/ = V$H-a"2",   or *s* ~ \ //-  n\                    (7)
Differentiating equation (7), squaring and replacing (/- by we have
Solving for <fa,
(8)
_ __..... a%
where i - V-1.   Integrating equation (8) we get
ix            t/
  cos"1'7